*n*: 10(

*n*+ 2) = 534

Exponentials & Logarithms Flashcards

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Solve the equation for *x*: 3x = 81

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Evaluate the logarithm: log4 (64)

log4 (64) = 3

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Evaluate the logarithm: log2 (32)

log2 (32) = 5

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Evaluate the logarithm: log5 (25)

log5 (25) = 2

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Evaluate the logarithm: log3 (81)

log3 (81) = 4

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State the base of this logarithm: log7 (49)

The base is 7.

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State the base of this logarithmic expression: log(7)

A log without a given base always has a base of 10.

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Exponential Growth

A quantity that increases with time in a manner that can be represented by the function *y* = *A**C**t*. *A* represents the initial amount at time *t* = 0 and *C* is a constant for the specific situation.

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Rewrite the equation so that it is solved for *x*: 7 = *e*(*x* - 3)

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Evaluate the expression: log(0.001)

log(0.001) = -3

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Rewrite the logarithmic expression in simpler form: 3log(*x*) - log(*y*)

The simplified form is log(*x*3/*y*)

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Rewrite the equation so that it is solved for *t*: 10(*t* - 7) = 3

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Rewrite the equation so that it is solved for *n*: 10(*n* + 2) = 534

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27 cards in set

How do you solve an equation that has a variable as an exponent? This set of flashcards will give you some practice problems on concepts related to exponential equations and logarithms. This includes rewriting logarithms using their properties, as well as the relationship between logarithms and exponents. You can also review a few exponential growth and decay problems.

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Rewrite the equation so that it is solved for *n*: 10(*n* + 2) = 534

Rewrite the equation so that it is solved for *t*: 10(*t* - 7) = 3

Rewrite the logarithmic expression in simpler form: 3log(*x*) - log(*y*)

The simplified form is log(*x*3/*y*)

Evaluate the expression: log(0.001)

log(0.001) = -3

Rewrite the equation so that it is solved for *x*: 7 = *e*(*x* - 3)

Exponential Growth

A quantity that increases with time in a manner that can be represented by the function *y* = *A**C**t*. *A* represents the initial amount at time *t* = 0 and *C* is a constant for the specific situation.

State the base of this logarithmic expression: log(7)

A log without a given base always has a base of 10.

State the base of this logarithm: log7 (49)

The base is 7.

Evaluate the logarithm: log3 (81)

log3 (81) = 4

Evaluate the logarithm: log5 (25)

log5 (25) = 2

Evaluate the logarithm: log2 (32)

log2 (32) = 5

Evaluate the logarithm: log4 (64)

log4 (64) = 3

Solve the equation for *x*: 3x = 81

Solve the equation for *x*: 125 = 5x

Solve the equation for *n*: 6n = 1296

Evaluate the equation: 5n = 20

The value of *n* is approximately 1.86.

Evaluate the equation: 3t = 27

Evaluate the expression: log3 (1)

log3 (1) = 0

Write the exponential function that represents the balance in a bank account after *t* years if your initial deposit is $2000 and the interest rate is 3%.

2000(1.03)*t*

Write the exponential function that represents the value of a motorcycle after 3 years if you bought it for $12,000 and it depreciates at a rate of 12% per year.

12000(0.88)3

Find the yearly rate of depreciation for the following situation. A used motorcycle was purchased for $8000. Five years later, its value has depreciated to $2621.

The rate of depreciation was approximately 20% per year.

Rewrite the logarithmic expression in simplest form: log(*x*3) + 2log(*x*) - 3log(*y*)

The simplified form is log(*x*5/*y*3).

Rewrite the logarithmic expression in simplest form: 2ln(*e* 2) + 3 ln*x*

The simplified form is 4 + ln(*x*3).

Give another way to write the expression: ln(*x*4)

ln(*x*4) can also be written as 4ln(*x*).

Evaluate the equation: ln(3) + ln(*x*) = 5

Evaluate the equation: 3ln(*x*) + ln(5) = 2ln(*x*) + 6

Give another way to write the expression: 3 + 2ln(*e*4) - 3ln(*t*)

11 + ln(1/*t*3)

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Math 101: College Algebra12 chapters | 95 lessons | 11 flashcard sets

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